1. Can anybody tell me what is the function of C1, C2, C3, C4 and how we choose the right value of those capacitors?
2. Can I use only one capacitor in the left and one capacitor in the right? What will be the difference (effect) ?
1) C2 is a bulk filter capacitor. C2 should be made as large as possible. A rough estimation often used is that its capacitance should be greater than 1000uF per ampere.
C1 and C3 are decoupling/bypassing capacitors. C1 and C3 should be 100nF.
C4 is an output bulk capacitor. You can use a capacitor with capacitance between 100uF and 4700uF.
2) You should use all of them. You can omit C4, but it's better if you don't. Use a smaller capacitor if you want, even as small as 10uF to 100uF, but use it.
Provides better removal of ripple and give better result. Scope showing that.
If I find material I will post here. Its from manufacturer datasheet and from one electronic magazine where they experiment with various cap and scope.
I assume you are referring to the physical construction of the board and the components layout where the decoupling capacitor must be placed very close to the regulator. As long as the capacitors are connected close enough, C3 or C4 closer shouldn't matter.